The Minimal Number of Generators of Wreath Products of Nilpotent Groups
نویسندگان
چکیده
Under the stronger assumption that B is either finite or abelian, this was proved by Yeo Kok Chye [7]. I n the simplest case not covered by his work, B has a cyclic subgroup o f finite index, and the problem can be translated to one concerning representations of such B over finite prime fields. During the last years of his life, S. D. Berman made substantial contributions to the representation theory of (not necessarily nilpotent) groups which have cyclic subgroups o f finite index. H e and the first author o f this paper repeatedly discussed the possibility that their results could be applied in the context of wreath products. Indeed, the results which are used in the proof below and which are more recent than Yeo Kok Chye [7] come from Berman and Buzdsi [2]. We do not know whether the theorem remains valid if one omits the condition that B i be finite. F o r example, let p and q be distinct primes, A a group of order p, and B the group defined by the presentation
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